If a tangent to the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` makes equal intercepts of length l on cordinates axes, then the values of l is

Options

A. `a^(2)+b^(2)`
B. `sqrt(a^(2)+b^(2))`
C. `(a^(2)+b^(2))^(2)`
D. None of these

Answer

B

Explanation

The equation of any tangent to the given
ellipse is `(x)/(a) cos theta + (y)/(b) sin theta =1`.
This line meets the coordinate axes at
`P((a)/(costheta')0)` and `Q(0,(b)/(sintheta))`.
`therefore (a)/(costheta)=1=(b)/(sintheta) implies costheta=(a)/(1)`
and `sintheta = (b)/(1)`
implies `cos^(2)theta+sin^(2)theta=(a^(2))/(1^(2))+(b^(2))/(1^(2))implies1^(2)=a^(2)+b^(2)`
`1=sqrt(a^(2)+b^(2))`